Composite laminates: nonlinear interlaminar stress analysis by multi-layer shell elements Original Research Article

An essential problem in dealing with composite laminates is an accurate prediction of interlaminar stresses playing an important role in the design, particularly in the failure analysis of these structures. The objective of the present paper is to develop a multi-layer shell-element family capable to deal with this aspect in the presence of strong nonlinearities. First a multi-director shell theory is presented on the basis of a quadratic approximation of the displacement field. A particular attention is given to the parametrization of the inextensible shell director in order to make the formulation accessible to finite rotations. This is accomplished by using Euler-angles as well as an updated rotation formulation. The single layer theory is then coupled with a multi-layer concept, which has been shown to be very predictive in dealing with complex through-thickness stress distributions. The constitutive relations are formulated so as to consider the particularities of composite materials. After standard linearization, shell equations are transformed into multi-layer finite shell elements using assumed strain concept and enhanced strain formulation as stabilization algorithms. The performance of the finite elements concerning various aspects is discussed on adequate examples.